Parallax

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Parallax is the displacement or difference in the visible position of the object seen along two different lines of sight, and measured by the angle or semi-angle of the slope between the two lines. This term comes from the Ancient Greek ?????????? (parallax) , meaning 'substitution'. Due to foreshortening, nearby objects show larger parallaxes of more distant objects when observed from different positions, so parallax can be used to determine distances.

To measure large distances, such as the distance of planets or stars from Earth, astronomers use the principle of parallax. Here, the term parallax is a semi-angle of tilt between two lines of sight to the star, as observed when the Earth is on the opposite side of the Sun in its orbit. This distance forms the lowest rung of the so-called "cosmic distance ladders", the first in a series of methods used by astronomers to determine the distance to celestial bodies, which serve as a basis for measuring other distances in astronomy forming a higher ladder from the stairs.

Parallax also affects optical instruments such as rifle scopes, binoculars, microscopes, and twin lens reflex cameras that view objects from slightly different angles. Many animals, including humans, have two eyes with overlapping visual fields that use parallax to gain depth perception; this process is known as stereopsis. In computer vision, the effect is used for computer stereo vision, and there are devices called parallax scouts that use them to find ranges, and in some variations as well as altitudes for the target.

A simple daily parallax example can be seen on a motor vehicle dashboard that uses a needle speedometer gauge. If viewed directly from the front, its speed can show exactly 60; but when viewed from the passenger seat the needle may seem to show a slightly different velocity, because of the viewing angle.

Video Parallax

Visual perception

When the eyes of other humans and animals are in different positions in the head, they present different views simultaneously. This is the basis of stereopsis, the process by which the brain exploits parallax due to different views of the eye to gain depth perception and estimate the distance to the object. Animals also use parallax motion , in which the animal (or just the head) moves to get a different angle of view. For example, pigeons (whose eyes do not have overlapping fields and therefore can not use stereopsis) shake their heads up and down to see the depth.

Parallax motion is exploited also in stereoscopy wobbles, computer graphics that provide depth cues through animation of the point of view switching rather than through binocular vision.

Maps Parallax

Astronomy

Parallax arises from a change in the viewpoint that occurs due to observer movements, observed, or both. The important thing is relative motion. By observing parallax, measuring angles, and using geometry, one can determine the distance. Astronomers also use the word "parallax" as a synonym for "distance measurement" by another method: see parallax (disambiguation) #Aronomy.

Parallax star

Parallax stars created by the relative motion between Earth and stars can be seen, in the Copernican model, arising from Earth's orbit around the Sun: the only stars appear to move relative to more distant objects in the sky. In geostatic models, star movement must be taken as real with the star oscillating in the sky by respecting the background stars.

Parallax stars are most often measured by using annual parallax , which is defined as the difference in star position as seen from Earth and the Sun, ie e. angles embedded in stars by the average radius of the Earth's orbit around the Sun. The parsec (3.26 light-years) is defined as the distance that the annual parallax is 1 arc second. The annual parallax is usually measured by observing the positions of stars at different times throughout the year as the Earth moves through its orbit. Annual parallax measurements are the first reliable way to determine the distance to nearby stars. The first successful measurements of star parallax were made by Friedrich Bessel in 1838 for the 61-cent Cygni using a heliometer. Parallax stars remain the standard for the calibration of other measurement methods. Accurate distance calculations based on parallax stars require measurement of distance from Earth to the Sun, now based on radar reflection from the planet's surface.

The angles involved in this calculation are so small that they are difficult to measure. The nearest star to the Sun (and thus the star with the largest parallax), Proxima Centauri, has a parallax of 0.7687 Â ± 0.0003 arcsec. This angle is roughly substituted by a 2-centimeter diameter object 5.3 kilometers away.

The fact that the star parallax is so small that it can not be observed at the time was used as a major scientific argument against heliocentrism during the early modern times. It is clear from Euclid's geometry that the effect can not be detected if the stars are distant, but for various reasons, such a gigantic distance seems utterly absurd: it is one of Tycho's major objections to Copernicus heliocentrism to be compatible with the absence of parallax observable stars, there must be a vast and impossible void between the orbit of Saturn (then the most distant known planet) and the eighth ball (the fixed stars).

In 1989, Hipparcos satellites were launched primarily to acquire enhanced parallax and proper movement to over 100,000 nearby stars, increasing the range of tenfold methods. Even so, Hipparcos is only capable of measuring parallax angles for stars up to about 1,600 light-years away, slightly more than one percent of the diameter of the Milky Way Galaxy. The Gaia mission of the European Space Agency, launched in December 2013, will be able to measure parallax angles to an accuracy of 10 microarcseconds, thus charting nearby (and potentially planetary) stars to distances tens of thousands of light-years from Earth. In April 2014, NASA astronomers reported that the Hubble Space Telescope, using spatial scans, can now accurately measure distances up to 10,000 light-years, a tenfold increase over previous measurements.

Distance measurement

Distance measurement by parallax is a special case of the principle of triangulation, which states that one can solve all sides and angles in a triangular network if, in addition to all angles in the network, the length of at least one side has been measured. Thus, careful measurement of the length of one baseline can improve the overall network triangulation scale. In parallax, triangles are very long and narrow, and by measuring both short sides (observer motion) and small top corners (always less than 1 arc seconds, leaving the other two closer to 90 degrees), long sides length (in practice equally) can be determined.

Denuncia asumsi sudutnya kecil (lihat derivasi di bawah), jarak ke objek (diukur dalam parsec) adalah kebalikan dari paralaks (diukur dalam detik busur): ${\ displaystyle d (\ mathrm {pc}) = 1/p (\ mathrm {arcsec}).} Â$ Misalnya, jarak that Proxima Centauri adalah 1/0.7687 = 1.3009 parsecs (4.243 â,¬ ly).

Parallax diurnal

Parallax diurnal is a parallax that varies with the Earth's rotation or with different locations on Earth. Moon and to a lesser extent, terrestrial planets or asteroids viewed from different viewing positions on Earth (at a given moment) may appear differently placed against a fixed star's background.

Crescent paralar

Lunar parallax (often short for horizontal parallax or horizontal horizontal parallax ), is a special case of parallax (diurnal): The moon, being a celestial body nearest, by far the largest parallax maximum of any celestial body, can exceed 1 degree.

The diagram (above) for the star parallax may illustrate the parallax of the moon as well, if the diagram is taken to be lowered and slightly modified. Instead of 'near star', read 'Moon', and instead of taking a circle at the bottom of the diagram to represent the Earth's orbital size around the Sun, take the Earth's globe size, and from circling the Earth's surface. Then, the parallax lunar (horizontal) amounts to a difference in the angular position, relative to the background of the distant star, from the Moon as seen from two different view positions on Earth: one of the display positions is the place from which the Moon can be seen directly above a certain moment (ie, seen along the vertical line in the diagram); and other viewing positions are the places from which the Moon can be seen on the horizon at the same time (ie, seen along one of the diagonal lines, from the Earth's surface position corresponding roughly to one of the blue dots on the modified diagram).

The lunar (horizontal) paralymes can alternately be defined as the angle deposited at the distance of the Moon by the radius of the Earth - equal to the angle p in the diagram when it is minimized and modified as mentioned above.

The horizontal parallax of the moon at any time depends on the linear distance of the Moon from Earth. The Earth-Moon's linear spacing changes continuously as the Moon follows its disturbed and elliptical orbit around the Earth. The range of variation in linear spacing is from about 56 to 63.7 Earth radius, corresponding to the horizontal parallax around the arc rate, but ranges from about 61.4 'to about 54'. Almanac Astronomy and similar publication of horizontal parallax tabulation of the moon and/or Linear spacing of Earth on periodic eg. the daily basis for the convenience of astronomers (and earlier, of the navigator), and the study of the manner in which these coordinates vary with time forms part of lunar theory.

Parallax can also be used to determine the distance to the Moon.

One way to determine the parallax of a month from a single location is to use a lunar eclipse. A full Earth shadow on the Moon has a radius of curvature that is clearly equal to the difference between the real radius of Earth and the Sun as seen from the Moon. These radii can be seen equal to 0.75 degrees, from which (with the radius of the sun clearly 0.25 degrees) we get a clear radius of Earth 1 degree. This resulted for Earth-Moon distance of 60.27 Earth radius or 384,399 kilometers (238,854 million) This procedure was first used by Aristarchus of Samos and Hipparchus, and later found its way into Ptolemy's work. The diagram on the right shows how the moon's parallax day appears on a geocentric and geostatic planet model where the Earth is at the center of the planetary system and does not rotate. It also illustrates the important point that parallax need not be caused by observer movements, contrary to some parallax definitions that say it, but may arise purely from observed motions.

Another method is to take two images of the Moon at the same time from two locations on Earth and compare the position of the Moon relative to the stars. By using the Earth orientation, two position measurements, and the distance between two locations on Earth, the distance to the Moon can be summed:

$Â\; Â{\displaystyle Â\; Â\; Â\; Â\; Â\; Â\; Â}$ _{                     d            me            s            t            a            n            c           e                                              m              o              o              n                                      =                        Â                             d                me               s               t               a               n                c               e        ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,                                                   o                 b                  s                 e                 r                 v                 e                 r                 b                 a                  s                 e        ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,        ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,          Â                 Â <                         (                             a               n               g                l               e        ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂ,                 )                                            {\ displaystyle \ mathrm {distance} _ {\ mathrm {moon}} = {\ frac {\ mathrm {distance} _ {mathrm {observerbase}}} {\ tan (\ mathrm {angle})}}}  Â}

This is the method called by Jules Verne in From Earth to the Moon :

Until then, many people do not know how one can calculate the distance that separates the Moon from Earth. Circumstances are used to teach them that this distance is obtained by measuring the parallax of the Moon. If the word parallax appears to amaze them, they are told that it is an angle bound by two straight lines flowing from both ends of the Earth's radius to the Moon. If they had any doubts on the perfection of this method, they immediately pointed out that not only this amount of distance meant for a total of two hundred and thirty four thousand three hundred and forty seven miles (94,330 leagues), but also that astronomers were not in error by more than seventy miles (? 30 leagues).

sun parallax

After Copernicus proposed his heliocentric system, with Earth in revolutions surrounding the Sun, it was possible to build a model throughout the Solar System without any scale. To ensure scale, it is only necessary to measure one distance in the Solar System, for example, the average distance from Earth to the Sun (now called astronomical unit, or AU). When found with triangulation, it is referred to as the sun parallax , the difference in the position of the Sun as seen from the center of the Earth and a point of radius of the Earth going, ie e, the angle subtended in the Sun by the average radius of the Earth. Knowing the parallax of the sun and the average Earth radius allows one to calculate the AU, the first step, a small long way to set the size and expansion of the visible age of the universe.

The primitive way to determine the distance to the Sun in terms of distance to the Moon has been proposed by Aristarchus of Samos in his book On the Size and Distance of the Sun and the Moon . He notes that the Sun, Moon, and Earth form a right triangle (with right angles on the Moon) at the time of the first or last quarter month. He then estimates that the Moon, Earth, Sun is 87 Â °. Using correct geometry but inaccurate observational data, Aristarchus concludes that the Sun is slightly less than 20 times farther than the Moon. The true value of this angle is close to 89 Â ° 50 ', and the Sun is actually about 390 times further. He points out that the Moon and Sun have almost the same angular size and therefore their diameter should be proportional to their distance from Earth. He concluded that the Sun is about 20 times larger than the Moon; This conclusion, though wrong, follows logically from the wrong data. It shows that the Sun is clearly larger than Earth, which can be taken to support the heliocentric model.

Although the results of Aristarchus are incorrect due to observational errors, they are based on true geometric parallax principles, and became the basis for the approximate size of the Solar System for nearly 2000 years, until the true Venus transit was observed in 1761 and 1769. This method was proposed by Edmond Halley on 1716, though he did not live to see the results. Venus transit usage is less successful than expected due to the black drop effect, but the resulting estimate, 153 million kilometers, is just 2% above the currently accepted value, 149.6 million kilometers.

Much later, the Solar System is 'scale' using asteroid parallaxes, some of which, like Eros, pass closer to Earth than Venus. In a favorable opposition, Eros can approach the Earth within 22 million kilometers. Both the 1901 and 1930/1931 contradictions were used for this purpose, the calculation of the final determination settled by Royal Astronomer Sir Harold Spencer Jones.

Also radar reflections, both from Venus (1958) and from asteroids, such as Icarus, have been used for the determination of sun parallax. Currently, the use of telemetry space links has solved this old problem. The currently accepted sun paralymx value is 8 ".794 143.

Parallax dynamic or move-cluster

Clusters of open stars of Hyades in Taurus extend over a large section of the sky, 20 degrees, that precise movements such as those derived from astrometry appear to converge with some precision to the northern perspective point of Orion. Combining the apparent (angular) right motion within a few seconds of the bow with the observed (absolute) pending movement as witnessed by the Doppler redshift of the star's spectral line, enables the estimate of the distance to the cluster (151 light-years) and its star members in the same way such as using annual parallax.

Dynamic parallaxes have sometimes also been used to determine the distance to the supernova, when an explosion-front optical wave is seen spreading through a dust cloud around it with a clear angular velocity, while the propagation speed is actually known as the speed of light.

Derivation

Untuk segitiga siku-siku,

${\ displaystyle \ tan p = {\ frac {1 {\ text {AU}}} {d}},} Â Â$

di mana ${\ displaystyle p}  ÂÂ$ adalah paralaks, 1 AU (149.600.000 km) adalah kira-kira jarak rata-rata dari Matahari ke Bumi, dan ${\ displaystyle d}  ÂÂ$ adalah jarak ke bintang. Menggunakan pendekatan sudut kecil (valid ketika sudutnya kecil dibandingkan dengan 1 radian),

${\ displaystyle \ tan x \ approx x {\ text {radians}} = x \ cdot {\ frac {180} {\ pi}} {\ text {degrees}} = x \ cdot 180 \ cdot {\ frac {3600} {\ pi}} {\ text {arcseconds}},}  ÂÂ$

jadi parallax, diukur dalam detik busur, adalah

${\ displaystyle p '' \ kira-kira {\ frac {1 {\ text {AU}}} {d}} \ cdot 180 \ cdot {\ frac {3600} {\ pi}}.} Â Â$

Jika paralaks adalah 1 ", maka jaraknya

${\ displaystyle d = 1 {\ text {AU}} \ cdot 180 \ cdot {\ frac {3600} {\ pi}} \ approx 206,265 {\ text {AU}} \ approx 3.2616 {\ text {ly}} \ equiv 1 {\ text {parsec}}.} Â Â$

Ini mendefinisikan parsec, unit yang nyaman untuk mengukur jarak menggunakan paralaks. Oleh karena itu, jarak, diukur dalam parsecs, hanyalah ${\ displaystyle d = 1/p} Â$ , ketika paralaks diberikan dalam detik busur.

Kesalahan

The exact parallax distance measurement has an associated error. However this error in the measured parallax angle is not directly translated into error for distance, except for relatively minor errors. The reason is that errors against smaller angles result in larger distance errors than errors toward larger angles.

Namun, perkiraan kesalahan jarak dapat dihitung dengan

${\ displaystyle \ delta d = \ delta \ left ({1 \ over p} \ right) = \ kiri | {\ parsial \ over \ parsial p} \ kiri ({1 \ over p} \ right) \ right | \ delta p = {\ delta p \ over p2}} Â Â$

where d is distance and p is parallax. The approximation is much more accurate for relatively small parallax errors against parallax than for relatively large errors. For meaningful results in star astronomy, Dutch astronomer, Floor van Leeuwen recommends that parallax errors be no more than 10% of the total parallax when calculating these error estimates.

Spatio-temporal parallax

From the improvement of the relativistic positioning system , parallax spatio-temporal which generalizes the general meaning of parallax in space has only been developed. Then, eventfields in spacetime can be inferred directly without the intermediate model of light flexing by large bodies such as those used in VAT formalism for example.

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Metrology

Measurements made by looking at the positions of some markers relative to something to be measured are subject to parallax error if the marker is some distance from the measuring object and not seen from the correct position. For example, if measuring the distance between two ticks on a line with a marked ruler on its upper surface, the thickness of the ruler will separate the marks from the tick. When viewed from a position not very perpendicular to the ruler, a clear position will shift and readings will be less accurate than capable rulers.

A similar error occurs when reading a pointer position against a scale in an instrument such as an analog multimeter. To help users avoid this problem, the scale is sometimes printed on a narrow strip of mirrors, and the user's eyes are positioned so that the pointer masks its own reflection, ensuring that the user's line of sight is perpendicular to the mirror and therefore scale. The same effect changes the reading speed on the car's speedometer by the driver in front of it and the passenger to the side, the value read from the graticule that is not in contact with the display on the oscilloscope, etc.

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Photogrammetry

Post aerial photos, when viewed through the stereo viewer, offer landscape and building stereo effects spoken. Tall buildings look 'upside down' in the direction far from the center of the photo. These parallax measurements are used to infer building heights, provided flight altitude and baseline distance are known. This is a key component for the photogrammetric process.

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Photography

Parallax error can be seen when taking photos with many types of cameras, such as double lens reflex camera and that includes viewfinders (like surveillance cameras). In such cameras, the eye sees the subject through various optics (viewfinder, or second lens) than through which the photo is taken. Since the viewfinder is often found above the camera lens, photos with parallax errors are often slightly lower than intended, a classic example is the image of a person with a head cut off. This problem is discussed in single lens reflex cameras, where the viewfinder sees through the same lens through which the photo is taken (with the help of a moving mirror), thus avoiding parallax errors.

Parallax is also a problem in image enhancement, as for panoramas.

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Landscape

Parallax affects the scene in many ways. On a scene suitable for small arms, bow in archery, etc. The distance between the observation mechanism and the hole or gun axis can cause significant errors when firing at close range, especially when firing on small targets. This difference is commonly referred to as "high vision" and compensated for (if required) through calculations that also take on other variables such as the bullet drop, windage, and the distance at which the target is expected to be. The height of sight can be used for the benefit of a "see-in" rifle for use in the field. A typical hunting rifle (.222 with a telescope view) seen at 75 m will be useful from 50m to 200m without further adjustment.

Optical spots

In parallax optical shots refers to the apparent movement of the reticle in relation to the target when the user moves his head laterally behind the vision (up/down or left/right), that is the error in which the reticle does not stay parallel to the optical axis of the vision itself.

In optical instruments such as telescopes, microscopes, or in telescopic sights used on small arms and theodolites, errors occur when optically imprecise is focused: the reticle will appear to move in relation to the object being focused on if one moves the head sideways. in front of the eyepiece. Some telescopic sight of firearms is equipped with a parallax compensation mechanism that essentially consists of a moving optical element that allows an optical system to project an object image at various distances and crosshairs viewfinder together in the exact same optical field. Landscape telescopes may not have parallax compensation as they can perform very acceptable without parallax refinements with visions that are permanently adjusted for the distance most suited to the intended use. The standard parallax factory standard adjustment range for hunting the telescopic sight is 100 times or 100 m to make it suitable for hunting that rarely exceeds 300 y/m. Some military-style telescopic targets and scenes without parallax compensation can be adjusted to free parallax in the range of up to 300 m/m to make it more suited to aim for longer ranges. Scopes for rimfires, shotguns, and muzzleloaders will have shorter parallax settings, typically 50 ms/m for rimfire scopes and 100 ms/m for shotgun and muzzleloaders. Scope for air rifles is very often found with adjustable parallaxes, usually in adjustable objective form, or AO. It can adjust as far as 3 meters (2.74 m).

Non-magnifying reflectors or "reflex" scenes have the ability to be theoretically "parallax-free." But since this scene uses parallel collimation light, this is only true when the target is at infinity. At a limited distance the movement of the eye perpendicular to the device will cause parallax movement in the reticle image in an exact relationship with the eye position in the light cylindrical column created by optical collimating. The flame scene, like some red dots, tries to correct this by not focusing the reticle on infinity, but at some distance, the target range designed in which the reticle will show very little movement due to parallax. Some produce reflective reflective models of the market which they call "parallax free," but this refers to optical systems that compensate for spherical aber lag, optical errors caused by spherical mirrors used in vision that can cause the reticle position to deviate from the optical axis of vision by changing position eye.

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Artillery fire

Because of the position of a field or naval artillery rifle, each has a slightly different perspective of the target relative to the location of the fire control system itself. Therefore, when aiming its gun at the target, the fire control system must balance the parallax to ensure that the fire of each pistol blends in on the target.

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Rangefinders

A partial spy or partial reconnaissance can be used to find the distance to the target.

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As a metaphor

In a philosophical/geometric sense: a real change in the direction of an object, caused by a change in an observation position that gives a new outline. Clear shift, or position difference, of an object, as seen from two different stations, or point of view. In contemporary writing parallax can also be the same story, or similar story from around the same time line, from a book that is told from a different perspective in another book. Words and concepts stand out in James Joyce's novel in 1922, Ulysses. Orson Scott Card also uses that term when referring to Ender's Shadow compared to Ender's Game.

This metaphor is triggered by the Slovenian philosopher Slavoj? I? Ek in his The Parallax View , borrowed the concept of "parallax view" from Japanese philosopher and literary critic Kojin Karatani. ? I? oak noted,

The philosophical touch to be added (to parallax), of course, is that the observed distance is not only subjective, since the same objects that are 'out there' are seen from two different attitudes, or points of view. More precisely, since Hegel will put it, subjects and objects are inherently mediated so that the 'epistemological' shift in the subject's perspective always reflects the ontological shift in the object itself. Or - to place it in Lacanese - the subject's view is always-already inserted into the perceived object itself, in the guise of the 'blind point,' which is 'in the object more than the object itself', the point of the object itself restores the view. Of course the picture is in my eyes, but I am also in the picture.

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See also

• Differences
• Bias Lutz Kelker
• Parallax mapping, in computer graphics
• Parallax scrolling, in computer graphics
• Refraction, a similar principle visually caused by water, etc.
• spectroscopic parallax
• Triangulation, where a point is calculated based on its angle from other known points
• Trilateration, where a point is calculated considering its distance from other known points
• Trigonometry
• Xallarap

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Note

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References

External links

• Instructions for having a background image on a web page using parallax effects
• The actual parallax project measures distance to the moon in 2.3%
• Sky at Night BBC Program: Patrick Moore demonstrates Parallax using Cricket. (Requires RealPlayer)
• The Berkeley Center for Cosmological Physics Parallax
• Parallax on educational websites, including fast distance estimates based on parallax using eyes and thumbs only
• Ã, "Sun, Parallax of the". The New Encyclopedia of Collier . 1921.

Source of the article : Wikipedia